Can I scale an object based on the relative distance to another object?
Driver Based Approach

Image below shows driver added to x scale of Empty.002.  The driver variable var is of Distance type and returns the distance between itself (Empty.002) and the master empty (Empty.001).  

The expression 4 - var if var &lt; 2 else 1 is set up such that if the empties are within 2 bu of each other the scale value is (4 - var) and if outside that range the scale is 1.  Change the numbers to suit.

Use the interface to copy this driver and paste into other scale fields.

When pasting into other empties scale fields, change the target of non master empty to match.